Optimizing planting density and nitrogen application to enhance profit and nitrogen use of summer maize in Huanghuaihai region of China

Low planting density and irrational nitrogen (N) fertilization are two common practices in conventional cropping of smallholder maize production in Huanghuaihai region of China. A 2-year field experiment was carried out to study the effects of N application and planting density on maize phenology, dry matter accumulation, profit, yield, N uptake and efficiency indices. The experiments included three N application levels (120 kg ha−1, N1; 180 kg ha−1, N2; 240 kg ha−1, N3) and three planting densities (60,000 plants ha−1, D1; 75,000 plants ha−1, D2; 90,000 plants ha−1, D3). Increasing N input and planting density delayed the physiological maturity and enhanced dry matter accumulation. Comparing with the traditional N3 level, grain yield and profit were kept stable at N2 level and decreased at N1 level, partial factor productivity of applied N (PFPN) and nitrogen efficiency ratio (NER) were increased with the decreasing of N level. Comparing with the traditional D1 density, grain yield, profit and PFPN were increased at D2 density and then kept stable at D3 density, NER was kept stable at D2 density and then decreased at D3 density. Based on the predicted maximum profit, the optimal combinations of N application and planting density were 199 kg ha−1 and 81,081 plants ha−1 in 2017, and 205 kg ha−1 and 84,782 plants ha−1 in 2018. The two optimal combinations had an increase of 17.6% for grain yield, 39.8% for PEPN, 3.6% for NRE than the traditional N3D1 treatment. Therefore, an appropriate combination of increased planting density with reduced N application could enhance profit and nitrogen use of summer maize in Huanghuaihai region of China.

The 2020 World Population Data Sheet indicates that world population is expected to increase from 7.8 billion in 2020 to 9.9 billion by 2050. This is likely to drastically increase food demand over the coming decades. As a staple crop in the world, maize cultivation is essential for yield improvement to meet the increasing food demand.
An evaluation of long-term studies has shown that 40 to 60% of crop yield can be attributed to fertilizer inputs 1,2 . Nitrogen (N) fertilizer is one of the most vital inputs in maize production 3 . Increasing N application rate is an effective way of obtaining high yield 4,5 . However, excessive fertilization often leads to not only low N use efficiency but also serious threats to environment and human health 3,6 . Besides N fertilizer, increasing planting density is a way for increasing grain yield, as it improved the ability of the crop canopy to capture water, nutrients and light 7,8 . However, crowded maize plants under high planting density, will result in resource competition between plants and consequently lead to a yield reduction per plant 9 . Therefore, optimal N input and planting density are critical for maize production.
Optimal planting density for high yield should be associated with an appropriate N application 10,11 . In super high-yield maize experiments, an appropriate increase of planting density and a reasonable reduction of N application can not only achieve high maize yield but also raise the N utilization efficiency in Northwest China 12 . In China, Huanghuaihai region is one major maize planting area, with planting area and the production occupying 34.7% and 36.8% of the whole China 13 , respectively. In this region, some problems exist with the traditional management practices of smallholder farming, such as low planting density and irrational N fertilizer 14,15 . Therefore, agricultural strategy that aims to obtain high profit and resource efficiency by means of optimizing planting density and N application rate is on demand. In this study, we hypothesized that, in Huanghuaihai region of China, high yield, high N use efficiency, and high economic return could be obtained by increasing www.nature.com/scientificreports/ planting density and optimizing N application rate. Therefore, the objectives of this study were to (1) determine the impacts of N application rate and planting density on maize phenology, dry matter, yield, profit, and N use; and (2) to determine the combination of planting density and N application rate which maximize the profit and N use based on smallholder farming in Huanghuaihai region in China.

Results
Days to tasseling, silking and physiological maturity. As shown in Table 1, planting density had significant effects on days to tasselling and silking in 2017, and both N rate and planting density had significant effects on days to tasselling, silking and physiological maturity in 2018 (Table 1). The decreasing N rate delayed the days to tasselling and silking, while shortened the days to physiological maturity especially in 2018. The significantly shortest period to tasseling (47.5 days) and silking (50.0 days) while longest period to physiological maturity (102.7 days) under N3 treatment were recorded according to 2 years' data. With increasing planting density, days to tasseling, silking and physiological maturity were delayed. The significantly longest period to tasseling (48.4 days), silking (51.2 days) and physiological maturity (102.9 days) under D3 treatment were recorded over two years.

Dry matter accumulation.
With the increase of either N rate or planting density, dry matter accumulation at 12-leaf stage, silking stage and physiological maturity stage were increased (Fig. 1). Compared to traditional N3 treatment, dry matter accumulation under N1 treatment showed a 11.6%, 12.2%, and 9.4% decrease in these three stages over 2 years. Compared to traditional D1 treatment, dry matter accumulation under D3 treatment showed a 16.8%, 28.4%, and 13.8% increase in these three stages over 2 years. The maximal dry matter accumulation was obtained with N3 × D3 treatment.
Maize yield and profit. N rate had significant effects on 1000-grain weight, grain yield and profit and didn't have significant effects on ear number and grains per ear, and planting density had significant effects on all these five indices ( Table 2). Increasing N rate caused 1000-grain weight, grain yield and profit increases with the peak showing at N2 treatment and remained stable at traditional N3 treatment. After averaging the effects of planting density, compared to N1 treatment, traditional N3 treatment increased 1000-grain weight, grain yield and profit by 2.6%, 5.3% and 2.7%, respectively. Increasing planting density resulted in an increased ear number, a decreased grains per ear and 1000-grain weight, an increased initially and then stable yield and profit.
After averaging the effects of N rate, ear number, grains per ear, 1000-grain weight, grain yield and profit of D3 treatment were 39.2%, − 8.7%, − 7.2%, 16.6% and 16.2% higher than the traditional D1 treatment, respectively. According to the 2 years' results, the greatest grain yield and profit was easily obtained for the combination of N2 or N3 and D2 or D3.
N uptake and N efficiency indices. Significant effects were observed from N rate and planting density on total N uptake, PFP N and NER. As N rate increased, the total N uptake was increased, while PFP N and NER were decreased. Traditional N3 treatment led to the maximal total N uptake and the minimal in PFP N and NER at all planting densities. Planting density had a different effect on these three indices. With the increased planting density, the total N uptake was increased, while PFP N was increased at D2 treatment and then kept stable at D3 treatment, NRE was kept stable at D2 treatment and then decreased at D3 treatment. Based on the 2 years' results, the high PFP N and NER were obtained at the combination of low N application and suitable planting density. www.nature.com/scientificreports/ Optimizing N application rate and planting density. To determine the optimal N application rate and planting density for profit, the relationships between N application and planting density and the profit was analysed (Fig. 2). The response surfaces that demonstrating the combined effect of N application and planting density on the profit were convex. Namely, with the increased N application and planting density, the profit was firstly increased, then reached a peak value, and finally decreased.
According to the second-order polynomials in Table 3, the predicted maximum profit was 3012 $ ha −1 (199 kg ha −1 and 81,081 plants ha −

Discussion
In this study, the plants at high planting density took longer time to tasseling, silking, and physiological maturity than the plants at low planting density. This indicated that dense planting may have slowed down plant www.nature.com/scientificreports/ development owing to more competition between plants 16 . A similar result was reported in earlier studies as dense population induced lengthening of the time to phenological characteristics [17][18][19] . In this study, increase in N input induced the advance in days to tasseling and silking. It may be due to quick growth under high nitrogen level. However, the plants took more time to physiological maturity with the increasing rate of N application. Namely, increasing N rate delayed the reproductive growth period of maize. It could be because the plants with more N application were remained green for longer period, which caused longer maturity period. The result was consistent with that of Shresth et al. 18 . The longer maturity period under high N and planting density conditions could be conducive to the increase of grain yield. In our study, high N input or high planting density enhances the dry matter accumulation and grain yield. There was a significant positive correlation between the dry matter and the grain yield 20 . Furthermore, grain yield was extremely affected by the assimilate allocation balance between vegetative and reproductive organs 11,21,22 . The longer reproductive growth period and more photosynthates availability with high N application induced the greater assimilates allocation to the seeds during grain filling, which improved grains per ear and grain weight. Increased plant density induced leaf senescence of lower leaf and then decreased the biomass accumulation, resulting in a lower yield per plant 23 . Also, greater inter-plant competition for light, water and nutrients with excessive planting density increased ear tip-barrenness which decreased grains per ear and grain weight. Yield improvement in response to higher density might be owing to maximize light interception during the vital period for grain set 24 . At the same time, the increased ear number per ha resulted from excessive density might offset the decrease of grains per ear and grain weight. These can be the reasons for the stable yield between D3 treatment and D2 treatment. Under high planting density, a moderate decrease of leaf source through leaf removal enhanced photosynthetic performance and improved the post-silking dry matter accumulation and harvest index, and thus the grain yield 25,26 . This indicates that grain yield at high density could achieve further improvement through optimal management practices. In this study, N3D3 obtained 16.1% higher grain yield than the traditional N3D1, a great yield increase of summer maize in smallholder fields in Huanghuaihai region of China.
According to the former results 20,27,28 , the dry matter was the driving force of the enhanced N uptake. In this study, the increases both N application rate and planting density improve the dry matter accumulation, which causes a high N absorption and assimilation level. Therefore, the increased N input or planting density maintained a high N uptake. In this study, PFP N and NER decreased with increased N rate. This is similar to the results of previous studies 12,15 . PFP N and NER were found to have a different change with planting density, and the medium D2 density had higher PFP N and NER than the low D1 density and high D3 density. This indicates that extremely high planting density is not helpful for the increase of PFP N and NER. This result is consistent with that of Zhang et al. 12 and can possibly be explained by the fact that excessive planting density results in a non-significant yield increase because of competition between plants and much more total N uptake.
Nutrient competition, mainly with respect to N, can be intensified by the increased planting density. In this study, a significant interaction between N application and planting density (Tables 2, 4) is observed. Therefore, it should be possible to optimize N application and planting density to regulate a trade-off between the three yield components (ear number, grains per ear and 1000-grain weight) to achieve high profit and N use. According to the two years' results in this study, when the predicted maximal profit of 2890 dollar ha −1 was achieved, N application rate and planting density were 201 kg ha −1 and 82,680 plants ha −1 , respectively. The yield, PFP N and NER under this condition were higher than the traditional N3D1 treatment. Therefore, reduced N application rate and increased planting density improved not only the profit but also grain yield, PFP N and NER for smallholder farming in Huanghuaihai region. Also, this study provides an important reference for determining the optimal combination of N application rate and planting density to obtain the highest profit under certain ecological conditions.

Conclusions
Maize profit and nitrogen use were affected by N application and planting density. Compared to traditional practices, the combination of 37.8% increase in planting density and 16.3% reduction in N application achieved the maximal profit. Under this optimal combination, increases of 17.6% for grain yield, 39.8% for PEP N , 3.6% for NRE were achieved than the traditional practices. Therefore, an appropriate increase of planting density and a reasonable reduction of N application can enhance profit, increase grain yield, reduce fertilizer input, and enhance nitrogen use of summer maize in Huanghuaihai region of China. Table 3. The quadratic polynomial trend surface equations, and yield, PFP N and NER. R 2 the coefficient of determination, x represents the N application rate (kg ha −1 ), y represents the planting density (plant ha −1 ), z represents the profit, GY represents the grain yield (t ha −1 ), PFP N represents partial factor productivity of applied N (kg kg −1 ), NER represents nitrogen efficiency ratio (%). **Represents significance at the 0.01 probability level.  29 . Precipitation and air temperature were measured by an automatic weather station (Fig. 3).
Experimental design and field management. The field experimental treatments were arranged in a split plot design with three replications. According to our survey and the present study 15,30,31 , traditional nitrogen rate and planting density in smallholder fields in Huanghuaihai region in China were about 240 kg ha −1 and 60,000 plants ha −1 , respectively. Based on these, the main plots were assigned to three N application rates (N1: 120 kg ha −1 ; N2: 180 kg ha −1 and N3: 240 kg ha −1 ), and subplots were designed to three planting densities (D1: 60,000 plants ha −1 ; D2: 75,000 plants ha −1 and D3: 90,000 plants ha −1  Sampling and measurements. The dates on which about 75% plants were at tasseling stage and silking stage were recorded. Physiological maturity was judged by the appearance of seed black layer. Days to tasseling, silking and physiological maturity were counted as the days from emergence date to tasseling date, silking date and physiological maturity date, respectively.
At 12-leaf, silking and physiological maturity, five whole plants were sampled to dry to a constant weight and determine dry matter. At physiological maturity, maize ears were collected from the middle two rows per plot to measure grain number per ear and 1000-grain weight. Finally, maize ears were harvested from central area of 14.4 m 2 per plot to measure ear number and grain yield. Profit was estimated using the following equation according to the method of Han et al. 20 .